In known goods-handling carts of this type, a single spring-effect element may be provided, as described in French patent No. 2 667 546, or two spring-effect elements may be provided which are located above respective ones of the stabilizing wheels, as is the case, for example, in the goods-handling carts sold by the company: BT (AKTIEBOLAGET BYGG-OCH TRANSPORTEKONOMI). In those known carts, each of the two stabilizing wheels is attached to a respective one of the two levers situated at the ends of the anti-roll bar. Under such conditions, when the cart leans to one side during a turn or on an inclined slope or indeed when tilted because of its load, the stabilizing wheel situated on the side towards which the cart is leaning exerts upwards vertical thrust on the associated lever. This vertical thrust has the effect of rotating the anti-roll bar about its longitudinal axis in its support bearings. As a result the spring-effect element(s), e.g. helical springs, are compressed, and the lever associated with the opposite stabilizing wheel, i.e. the wheel on the side that is opposite from the side towards which the cart is leaning, also rotates with the anti-roll bar. Consequently said opposite stabilizing wheel rises and looses contact with the ground. Thus, it is no longer steered by its contact with the ground and since it is free to swivel, it can swivel into any orientation while it is no longer in contact with the ground. Consequently, when the cart returns to its normal position, at the instant the stabilizing wheel regains contact with the ground, it may be oriented perpendicularly to the travel direction of the cart. Should that happen, the swivelling wheel or the elements mounting it on the chassis of the cart can be subjected to considerable damage.